A049299 a(n) = Product_{k = 0..n-1} (a(k) + a(n-1-k)), with a(0) = 1.

1, 2, 9, 400, 19456921, 1101216948902114953248, 76796373204229717290826972582321984854855228022915711475735049

Offset: 0

Author

Leroy Quet

Keywords

• easy
• nonn

Examples

			a(3)=400 because 400=(1+9)*(2+2)*(9+1).
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..8

Crossrefs

Cf. A000108 (Catalan numbers) where a(0) = 1, a(n) = Sum_{k=0..n-1} a(k)*a(n-k), A000012 (constant 1) where a(0) = 1, a(n) = Product_{k=0..n-1} a(k)*a(n-k) and A025192 (2*3^(n-1)) where a(0) = 1, a(n) = Sum_{k=0..n-1} a(k)+a(n-k). - Henry Bottomley, May 16 2000

Programs

PARI

a(n)={my(v=vector(n+1)); for(n=1, #v, v[n]=prod(k=1, n-1, v[k]+v[n-k])); v[#v]} \\ Andrew Howroyd, Jan 02 2020

Formula

lim_{m -> oo} log(a(m+1))/log(a(m)) exists and equals 3. - Roland Bacher, Sep 06 2004.

Extensions

Offset corrected and terms a(6) and beyond from Andrew Howroyd, Jan 02 2020